相关论文: Matching in a family of piecewise affine maps

The Chirikov standard map family is a one-parameter family of volume-preserving maps exhibiting hyperbolicity on a `large' but noninvariant subset of phase space. Based on this predominant hyperbolicity and numerical experiments, it is…

Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any…

We investigate an simple evolutionary game of sequences and demonstrate on this example the structure of fitness landscapes in discrete problems. We show the smoothing action of the genotype-phenotype mapping which still makes it feasible…

We give a hierarchy of many-parameter families of maps of the interval [0,1] with an invariant measure and using the measure, we calculate Kolmogorov--Sinai entropy of these maps analytically. In contrary to the usual one-dimensional maps…

The limit of small entropy production is reached in relaxing systems long after preparation, and in stationary driven systems in the limit of small driving power. Surprisingly, for extended systems this limit is not in general the…

The problem of membrane topology in the matrix model of M-theory is considered. The matrix regularization procedure, which makes a correspondence between finite-sized matrices and functions defined on a two-dimensional base space, is…

A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its…

Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…

The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic,…

Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…

It is often stated that if one is presented with a snapshot of the positions of the molecules of a glass and one of a liquid, one is unable to tell the difference. Here we argue instead that given several such snapshots taken over a…

We study betweenness preserving mappings (we call them \emph{monotone}) defined on subsets of the plane. Once the domain is a convex set, such a mapping is either the restriction of a homography, or its image is contained in the union of a…

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as \emph{simplicity bias}. By viewing…

In this paper we develop a new approach for studying overlapping iterated function systems. This approach is inspired by a famous result due to Khintchine from Diophantine approximation. This result shows that for a family of limsup sets,…

Many biological systems perform close to their physical limits, but promoting this optimality to a general principle seems to require implausibly fine tuning of parameters. Using examples from a wide range of systems, we show that this…

From a two-agent, two-strategy congestion game where both agents apply the multiplicative weights update algorithm, we obtain a two-parameter family of maps of the unit square to itself. Interesting dynamics arise on the invariant diagonal,…

We consider a prototypical two-parameter family of invertible maps of $\mathbb{Z}^2$, representing rotations with decreasing rotation number. These maps describe the dynamics inside the island chains of a piecewise affine discrete twist map…

We study the asymptotic behavior of a family of functionals which penalize a short-range interaction of convolution type between a finite perimeter set and its complement. We first compute the pointwise limit and we obtain a lower estimate…

We have studied the local and boundary behavior of mappings satisfying one estimate of the distortion of the modulus of families of paths. In particular, we have obtained conditions under which the families of the indicated mappings are…